Self Starting Method and an Apparatus for Sensorless Commutation of Brushless CD Motors

ABSTRACT

A method and apparatus for electronic control of a direct current motor is disclosed based upon a sensorless commutation technique using voltage vector analysis. A voltage vector is produced by addition of supply phase voltage vectors of energized windings with the back-electromotive force vector of the unenergized winding. The resultant voltage vector rotates at the same speed as the rotor and possesses rotor position information used to commutate phase windings. The angle that the resultant voltage vector makes with the real axis is measured to commutate the phase windings. By parking the rotor in a predetermined position, this technique can be used to efficiently start the motor from rest and commutate phase windings during normal operation.

RELATED APPLICATIONS

This application is a Divisional Application of application Ser. No.11/813,453 titled “A SELF STARTING METHOD AND AN APPARATUS FORSENSORLESS COMMUTATION OF BRUSHLESS DC MOTORS,” filed on Jul. 6, 2007, anational stage filing under 35 USC 371 of PCT Application No.PCT/TT2005/000001, titled “A SELF STARTING METHOD AND AN APPARATUS FORSENSORLESS COMMUTATION OF BRUSHLESS DC MOTORS” filed on Sep. 1, 2005which claims priority to Trinidad and Tobago Application No.TT/A/2005/00001, titled “A SELF STARTING METHOD AND AN APPARATUS FORSENSORLESS COMMUTATION OF BRUSHLESS DC MOTORS” filed on Jan. 7, 2005.Each of these references is hereby incorporated by reference herein.

BACKGROUND

1. Field of the Invention

The present invention which is self-starting, relates to the field ofbrushless permanent magnet motors and more particularly to brushlesspermanent magnet motors in DC operation, not having position sensors fordetecting the rotational position of a permanent magnet motor.

2. Discussion of Related Art

The present invention relates to a technique for efficient starting andcommutation of a multi-phase Brushless DC motor under all loadconditions without rotor position sensors.

The Brushless DC (BLDC) motor is an inverted brush DC motor inconstruction. The armature coils in the brush dc motor are transferredto the stator in the BLDC motor and the fixed magnets in the brush DCmotor are transferred to the rotor in the BLDC motor. This designeliminates the need for the mechanical commutators and brushes whichfunction is executed by transistors which act as switches.

The motor is powered by turning on two transistors in the switchingarrangement, which connect two of the three phase windings to the DCsupply for ⅙ of the time in an electrical cycle. Rotation of the rotormagnets induces voltages in the three stator phase windings andefficient operation of this motor is ensured by energizing the two phasewindings which are experiencing a constant BEMF. This ensures that mostof the electrical input power is converted to mechanical power with theminimum copper loss in the process. The BEMF generated in theunenergized winding provides very useful information of rotor position,provided the energy which was stored in its magnetic field has beendissipated, thereby completing the commutation of the unenergizedwinding.

Since the BEMF of a winding is dependent on the rotor position, rotorposition information must be known in order to energize a pair of statorwindings. Rotor position information for the purpose of stator windingenergization is obtained with the use of Hall Sensors in U.S. Pat. No.3,783,359, Optical Encoders and Resolvers in sensored commutationtechniques and with the use of the BEMF Zero Crossing in U.S. Pat. No.4,027,215, BEMF Integration in U.S. Pat. No. 4,169,990 and BEMF ThirdHarmonic in U.S. Pat. No. 4,912,378 in sensorless commutationtechniques. Many versions of the heretofore cited three sensorlesscommutation techniques have been developed using elaborate electroniccircuitry and having some innovations over those said patents asaforementioned.

The Hall Sensor Commutation technique requires three Hall sensors andsupporting components wired on a printed circuit board, a DC powersupply, space in the motor body and a sensing magnet with similarpolarity to that of the rotor magnet and properly aligned with the rotormagnet. Accurate positioning of the Hall sensors is required and fiveconnection wires are required to supply rotor position information. Thissaid commutation technique increases the cost, size and weight of themotor and decreases the reliability of the system.

Optical encoders and resolvers are connected to the motor shaft forproviding rotor position information via electrical wires connected tothem. Unlike the Hall sensors, these said encoders do not produce rotorposition information at standstill. These two said rotor positioninformation techniques add substantial cost to the motor and utilise oneend of the motor shaft.

These said three sensorless commutation techniques, in addition toincreasing the cost of the motor also reduce the reliability of motoroperation either in failure of the sensing devices due to the harshenvironment in which the sensors often operate or by damage to theelectrical wires carrying the rotor position information.

The three sensorless commutation techniques as aforementioned have theirindividual drawbacks but they all suffer from one major drawback in thatthey are not self-starting and a starting technique must be employed torun the motor up to a speed where the BEMF is large enough for thesensorless technique to be implemented. In addition to these saidsensorless techniques not being self-starting, they sometimes do notsense commutation points due to noise in the BEMF signal and are unableto operate properly at low speeds when the BEMF signal generated issmall.

Starting methods have been presented in U.S. Pat. No. 4,694,210, U.S.Pat. No. 5,343,127 and U.S. Pat. No. 6,642,681 for sensorlesscommutation of Brushless DC motors. However, these said startingtechniques are cumbersome and are different from the commutationtechnique used when the motor is running.

SUMMARY

The present invention is based fundamentally on the existence of voltagevectors that occupy the stator space of a Brushless DC motor. The sum ofthe two applied phase voltage vectors and the BEMF phase vector of theunenergized phase winding, produce the resultant voltage vector, theangle of which made with the real axis is used to commutate phasewindings for efficient motor operation. This sensorless commutationtechnique utilizing voltage vectors and more precisely, the angle madeby the resultant voltage vector is innovative, ground-breaking andrevolutionary to the field of sensorless commutation of Brushless DCmotors. It utilizes the same Digital Signal Processor (DSP) which isused to supply the control waveforms for motor energization, to computethe phase and resultant voltage vectors and the angle that the resultantvoltage vector makes with the real axis, thereby eliminating the needfor additional signal conditioning electronic circuitry, whichcomponents undergo aging and fail with time, thus decreasing thereliability of the system.

With reference to the present invention, the sensorless commutationtechniques of the prior art all use scalar voltages and electronicsignal conditioning circuitry to accomplish their task. Therefore, theuse of vector voltages and the manner in which they are produced, hasdistanced this sensorless commutation technique from all other knowntechniques hitherto presented thus far.

The vector method of analysis has been first applied to electricalmachines by Kovacs and Racz and is widely used in the analysis ofalternating current electrical machines. As the name implies, aBrushless DC motor has been considered as a DC motor and DC motoranalysis has always been applied to motor operation when two phasewindings are energized. However, when motor operation is examined overan electrical cycle of operation, it is clear from the supplied voltagesand currents, that ac motor operation is in effect, and as aconsequence, vector analysis could be applied to the motor's operation.This said method of vector analysis as presented by Kovacs, althoughmathematically correct, raises some fundamental issues when applied toelectrical machine analysis. These said issues have remained unresolvedfor over 45 years since they were not deemed to be important to thevector analysis of induction and synchronous machines. However, thesevery issues are of significance if vector analysis has to be applied toBrushless DC motors and must of necessity be addressed for thesuccessful application of voltage vectors to commutate these saidmotors.

With respect to the internalisation of the modus operandi of the presentinvention, the issues in question are as follows:

-   (a) It was stated that a current flowing through a stator phase    winding produces a current vector along the winding's magnetic axis.    However, the mechanism and process by which a scalar current flowing    through the winding produces a vector current along the winding's    magnetic axis were not presented;-   (b) It was stated as well, that the magnitude of the scalar current    was equal to that of the vector current, but no scientific proof was    given for this equality;-   (c) The current vectors produced by each phase winding of a    three-phase two-pole stator, whose phase windings are separated from    each other by 120 electrical degrees were added vectorially to    produce the resultant current vector as shown in the equation,

{right arrow over (i _(r))}=i _(a) +{right arrow over (a)}i _(b)+{rightarrow over (a ²)}i _(c)

-   -   where, {right arrow over (i_(r))} represents the resultant        current vector, i_(a), i_(b) and i_(c) are the instantaneous        currents in phase windings aa′, bb′ and cc′ respectively and        {right arrow over (a)} and {right arrow over (a²)} are unit        position vectors. It was then inferred that the resultant        voltage vector could be produced in a similar manner by the        vector addition of the voltage vectors produced by each phase        winding as shown in the equation

{right arrow over (v _(r))}=v _(a)+{right arrow over (a)}v _(b)+{rightarrow over (a ²)}v _(c)

-   -   where, {right arrow over (v_(r))} is the resultant voltage        vector and v_(a), v_(b) and v_(c) are the instantaneous values        of phase voltages for windings aa′, bb′ and cc′ respectively.        Although the above equation exists, it was not shown or proven        how scalar supply phase voltages were transformed to vector        supply phase voltages and how these vector supply phase voltages        lie on the winding's magnetic axis;

-   (d) And finally, the multiplication of a scalar voltage differential    equation for a phase winding by a unit position vector representing    the direction of the magnetic axis of that winding, although    mathematically correct, fails to show how these scalar voltages are    physically transformed into vector quantities. For example, Kovacs    presented the scalar voltage differential equation for winding bb′    as

$v_{b} = {{i_{b}R_{b}} + \frac{\lambda_{b}}{t}}$

-   -   where, v_(b), i_(b) and λ_(b) are the scalar phase voltage,        scalar phase current and scalar phase flux linkage respectively        and R_(b) the stator phase resistance for winding bb′. The        aforementioned equation was then multiplied by {right arrow over        (a)}, the unit position vector indicating the direction of the        positive magnetic axis of winding bb′, producing the equation,

${\overset{\rightarrow}{a}v_{b}} = {{\overset{\rightarrow}{a}i_{b}R_{b}} + {\frac{{\overset{\rightarrow}{a}}\lambda_{b}}{t}.}}$

-   -   Although the foregoing equation is mathematically correct, there        has been no reduction to practice by Kovacs to demonstrate how        scalar voltages i_(b)R_(b) and

$\frac{\lambda_{b}}{t}$

were transformed to vector quantities in the said equation.

It was stated by Kovacs that “the vector method is a simple butmathematically precise method; furthermore, it enables us to see thephysical background of the various phenomena.” The inventor concurs withthe said statement, however, the aforementioned points raised in (a) to(d), although being mathematically correct, have not utilised thephysical background of the various phenomenon in the development of thevarious vector quantities and equations. As a result, the optimal powerand benefits of the vector method, to be derived in the analysis ofthree-phase machines, whereby the physical background of the variousphenomenon may be observed, was not realized as a result of the issuespresented heretofore in (a) to (d).

A cross-sectional view of the stator windings of a two-pole, three-phaseBrushless DC motor is shown in FIG. 1 a. The phase windings are shown tobe displaced from each other by 120 degrees and the positive directionof current flow through each winding is upwards through the non-primedside and downwards through the primed side of each winding. Using thisconvention of current flow through the windings, positive magnetic axisfor phase winding aa′ (4), positive magnetic axis for phase winding bb′(8) and positive magnetic axis for phase winding cc′ (9) are shown inFIG. 1 a, along which all magnetic quantities exist.

The analysis of electromagnetic systems has traditionally been performedwith the production of two circuits, an electrical circuit forelectrical analysis and a magnetic circuit for magnetic analysis.However, quantities in the electrical circuit affect quantities in themagnetic circuit and vice-versa. As a result of the dependence of bothelectrical and magnetic circuits on each other, the development of anequivalent circuit containing both electrical and magnetic quantitieswould prove to be very useful in the analysis of electromagneticsystems. Since the three-phase stator is an electromagnetic system, thenthe application of an equivalent circuit containing both electrical andmagnetic quantities would be a powerful tool in the vector analysisapproach of said electromagnetic system. For this analysis, one phasewinding of the three-phase stator, winding aa′ was selected foranalysis. This winding is represented by its center conductors andcurrent flow through the winding is in the positive direction as shownin FIGS. 1 b-1 c. The phase winding possesses resistance which is anelectrical quantity and inductance which is both an electrical and amagnetic quantity. The winding resistance R_(a) being an electricalquantity is removed from the winding together with

${L_{a}\frac{i_{a}}{t}},$

which is an electrical voltage. These two quantities R_(a) and

$L_{a}\frac{i_{a}}{t}$

are placed on the left electric side of the circuit with the supplyvoltage V_(an). The winding with its magnetic quantities and electriccurrent are on the right side of the circuit in FIG. 1 b. This processseparates the electrical voltage quantities from the magneticquantities. The electric scalar current i_(a), which leaves the electriccircuit, flows through the winding and produces vector magnetic fieldintensity {right arrow over (H_(a))} along the positive magnetic axis ofwinding aa′ (4) as shown in FIG. 1 b.

The magnitude of {right arrow over (H_(a))} is obtained by AmperesCircuital Law and is given by

$\frac{i_{a}l_{a}}{Na},$

where l_(a) is the length of the path of {right arrow over (H_(a))} andN_(a) is the number of turns of winding aa′. The magnetic fieldintensity {right arrow over (H_(a))} produces a flux density {rightarrow over (B_(a))}, which is co-linear with {right arrow over (H_(a))},and which magnitude is given by μ|{right arrow over (H_(a))}|, where μis the permeability of the medium through which {right arrow over(B_(a))} flows. Flux density {right arrow over (B_(a))} produces flux{right arrow over (φ_(a))}, which is also co-linear with {right arrowover (B_(a))} and which magnitude is given by |{right arrow over(B_(a))}|A_(a) where A_(a) is the cross-sectional area of concern. Theflux linked with winding aa′ is given by {right arrow over (λ_(a))},which is co-linear with {right arrow over (φ_(a))} and which magnitudeis given by |{right arrow over (φ_(a))}|N_(a). The flux linkage {rightarrow over (λ_(a))} provides a current vector {right arrow over (i_(a))}which magnitude is given by

$\frac{\overset{->}{\lambda_{a}}}{L_{a}}$

which is co-linear with {right arrow over (λ_(a))}. Hence magneticquantities {right arrow over (H_(a))}, {right arrow over (B_(a))},{right arrow over (φ_(a))}, {right arrow over (λ_(a))} and currentvector {right arrow over (i_(a))} all lie along the positive magneticaxis of winding aa′ (4) and are spatial vector quantities possessingboth magnitude and direction.

It must be noted in FIG. 1 c that the electric and magnetic circuits areshown to be joined together but separated from each other by thevertical dotted line shown in said. Since current vector {right arrowover (i_(a))} leaves the magnetic circuit, a current vector {right arrowover (i_(a))} must also enter the series connected magnetic circuit ofFIG. 1 c. In addition, since the electric and magnetic circuits areconnected in series, this implies that the scalar electric current{right arrow over (i_(a))} is of the same magnitude as the vectormagnetic current {right arrow over (i_(a))}. The separation of electricand magnetic circuits is shown by the dotted vertical line, with themagnetic current vector {right arrow over (i_(a))} taking up a scalarvalue when it enters the electric circuit and the scalar electriccurrent {right arrow over (i_(a))} taking up a vector magnetic valuewhen it enters the magnetic circuit as shown in FIG. 1 c. Hence themagnetic axis of winding aa′ (4) completes the electric circuit makingi_(a) and |{right arrow over (i_(a)|)} of same magnitude.

If i_(a) is changing, then the effect of the magnetic circuit on theelectric circuit is seen in the voltage

$L_{a}\frac{i_{a}}{t}$

which opposes the current i_(a). Since the magnitude of i_(a) and {rightarrow over (i_(a))} are equal and {right arrow over (i_(a))} lies alongthe winding's magnetic axis, then the voltages i_(a)R_(a) and

$L_{a}\frac{i_{a}}{t}$

can be referred to the magnetic axis of winding aa′ (4) without changingtheir magnitudes. The vector summation of {right arrow over(i_(a))}R_(a) and

$L_{a}\frac{\overset{\rightarrow}{i_{a}}}{t}$

along the magnetic axis of winding aa′ (4), produces the supply voltagevector {right arrow over (V_(an))} along the magnetic axis of windingaa′ (4). Applying Kirchhoff's voltage law to the electric and magneticsides of said FIG. 1 c yields,

$V_{an} = {{i_{a}R_{a}} + {L_{a}\frac{i_{a}}{t}\mspace{14mu} {for}\mspace{14mu} {the}\mspace{14mu} {electric}\mspace{14mu} {side}}}$and$\overset{\rightarrow}{V_{an}} = {{\overset{\rightarrow}{i_{a}}R_{a}} + {L_{a}\frac{\overset{\rightarrow}{i_{a}}}{t}\mspace{14mu} {for}\mspace{14mu} {the}\mspace{14mu} {magnetic}\mspace{14mu} {{side}.}}}$

The production of an equivalent circuit containing electric and magneticquantities for the electromagnetic system represented by one phasewinding of a three-phase stator, clarifies the issues raised in (a) to(d) as heretofore mentioned. A summary of the benefits gained from theabove analysis utilizing the equivalent circuit containing electric andmagnetic quantities as it relates to the issues raised in (a), (b) and(d) are as follows:

-   -   (i) It shows, that when a scalar current i_(a) of an        electromagnetic system, leaves the electric circuit and enters        the magnetic circuit, it is converted into a vector quantity        {right arrow over (i_(a))} of the same magnitude as the scalar        current. This is a result of the series nature of the electric        and magnetic circuits resulting in the same magnitude of both        scalar and vector currents. The location of the current vector        is along the magnetic axis of the magnetic circuit because all        quantities of the magnetic circuit are located on its axis;    -   (ii) Since the vector current is of the same magnitude as the        scalar current and this said current vector lies on the magnetic        axis of the winding, then scalar voltages i_(a)R_(a) and

$L_{a}\frac{i_{a}}{t}$

can be referred to the magnetic axis of the winding becoming {rightarrow over (i_(a))}R_(a) R_(a) and

$L_{a}\frac{\overset{\rightarrow}{i_{a}}}{t}$

respectively, with these vector voltages being of the same magnitude astheir scalar counterparts. In addition, since the sum of the scalarvoltages i_(a)R_(a) and

$L_{a}\frac{i_{a}}{t}$

in the electric circuit results in the scalar supply voltage, then thesum of the vector voltages {right arrow over (i_(a))}R_(a) and

$L_{a}\frac{\overset{\rightarrow}{i_{a}}}{t}$

results in the vector supply voltage, which is of the same magnitude asthe scalar supply voltage;

-   -   (iii) In addition to showing the process by which scalar        voltages are referred to the magnetic circuit of the        electromagnetic system, the analysis produces a scalar and a        vector voltage differential equation. If scalar analysis is        being performed, then the scalar voltage differential equation        is utilized, while if vector analysis is being performed on the        electromagnetic system formed by the stator, then the vector        voltage differential equation would be utilized;    -   (iv) Both scalar and vector voltage differential equations        reveal the same magnitude of voltages and current; however, as        will be shown later, the vector voltage and current variables        together with the vector magnetic variables would be used to        reflect the physical background of the various phenomenon        occurring in the machine.

The application of the aforementioned technique to the three-phase,two-pole Brushless DC motor stator as shown in FIG. 1 a, which phasewindings are displaced from each other by 120 electrical degrees,produces the magnetic and electric quantities of each phase vectoriallyalong the positive magnetic axis for phase winding aa′ (4), positivemagnetic axis for phase winding bb′ (8) and positive magnetic axis forphase winding cc′ (9) as shown in FIG. 1 d.

Each magnetic or electric phase variable can now be added vectorially toproduce the resultant of that variable. Hence the resultant magneticfield intensity {right arrow over (H_(res))}, flux density {right arrowover (B_(res))}, flux {right arrow over (φ_(res) )} flux linkage {rightarrow over (λ_(res))}, current vector {right arrow over (i_(res))},stator resistance voltage drop {right arrow over (i_(res))}R_(s),inductance voltage

$L_{s} = \frac{\overset{\rightarrow}{i_{res}}}{t}$

and supply voltage {right arrow over (v_(res))} are given by the vectoraddition of their phase variables shown on the magnetic axes in FIG. 1d, which yield

$\overset{\rightarrow}{H_{res}} = {H_{a} + {\overset{\rightarrow}{a}H_{b}} + {\overset{\rightarrow}{a^{2}}H_{c}}}$$\overset{\rightarrow}{B_{res}} = {B_{a} + {\overset{\rightarrow}{a}B_{b}} + {\overset{\rightarrow}{a^{2}}B_{c}}}$$\overset{\rightarrow}{\varphi_{res}} = {\varphi_{a} + {\overset{\rightarrow}{a}\varphi_{b}} + {\overset{\rightarrow}{a^{2}}\varphi_{c}}}$$\overset{\rightarrow}{\lambda_{res}} = {\lambda_{a} + {\overset{\rightarrow}{a}\lambda_{b}} + {\overset{\rightarrow}{a^{2}}\lambda_{c}}}$$\overset{\rightarrow}{i_{res}} = {i_{a} + {\overset{\rightarrow}{a}i_{b}} + {\overset{\rightarrow}{a^{2}}i_{c}}}$${\overset{\rightarrow}{i_{res}}R_{s}} = {{i_{a}R_{a}} + {\overset{\rightarrow}{a}i_{b}R_{b}} + {\overset{\rightarrow}{a^{2}}i_{c}R_{c}}}$${L_{s}\frac{\overset{\rightarrow}{i_{res}}}{t}} = {{L_{a}\frac{i_{a}}{t}} + {\overset{\rightarrow}{a}L_{b}\frac{i_{b}}{t}} + {\overset{\rightarrow}{a^{2}}L_{c}\frac{i_{c}}{t}}}$$\overset{\rightarrow}{v_{res}} = {v_{a} + {\overset{\rightarrow}{a}v_{b}} + {\overset{\rightarrow}{a^{2}}v_{c}}}$

In the said aforementioned equations, {right arrow over (a)} and {rightarrow over (a²)} are unit vectors representing the position of thepositive magnetic axes of windings bb′ and cc′ respectively and themagnetic and electric variables on the right hand side of theseequations are the instantaneous values of these variables for theparticular winding. The application of Kirchhoff's Law to the vectorvoltages on each magnetic axis yields,

$v_{a} = {{i_{a}R_{a}} + \frac{\lambda_{a}}{t}}$$\overset{\rightarrow}{v_{b}} = {{\overset{\rightarrow}{a}v_{b}} = {{\overset{\rightarrow}{a}i_{b}R_{b}} + {\overset{\rightarrow}{a}\frac{\lambda_{b}}{t}}}}$$\overset{\rightarrow}{v_{c}} = {{\overset{\rightarrow}{a^{2}}v_{c}} = {{\overset{\rightarrow}{a^{2}}i_{c}R_{c}} + {\overset{\rightarrow}{a^{2}}{\frac{\lambda_{c}}{t}.}}}}$

The aforementioned three equations reveal that both the phase vectorsupply voltage and the resultant voltage vector of the three phasewindings were obtained by vector addition of vector voltages that existon the axes of the phase windings of FIG. 1 d.

In summary therefore, the aforementioned proofs and clarification of theabove issues with respect to the present invention have revealed theexact location and magnitude of each phase voltage vector, which is ofcritical importance in the proposed sensorless commutation technique.

Concomitant upon the foregoing, therefore, it is a first object of thepresent invention to effectively mitigate known disadvantages of theprior art.

It is a second object of the present invention to provide a method andan apparatus for an invention which is based on the existence of voltagevectors which occupy the stator space of a Brushless DC motor.

Yet a further object of the present invention is the provision of amethod and an apparatus for the demonstration of how scalar supply phasevoltages are transformed to vector supply phase voltages and thepositioning of these said voltages on the winding's magnetic axis.

Still a further object of the present invention is to provide a methodand an apparatus, which is used to supply the control waveforms formotor energization by computing the phase and resultant voltage vectorsand the angle which the resultant voltage vector makes with the realaxis, thereby eliminating the need for additional signal conditioningelectronic circuitry.

Moreover, still yet a further object of the present invention is toprovide a method and an apparatus which optimally performs the techniqueof the self-starting ability, from rest under no-load and loadconditions, of the De Four BEMF Space Vector Resolver, said techniquebeing hitherto unknown, among all other sensorless techniques of theprior art, used for the commutation of Brushless DC motors.

Finally, another object of the present invention is to determine theenergization sequence for a particular direction of motor rotation, withthe intention of producing uni-directional and continuous torqueproduction.

BRIEF DESCRIPTION OF THE DRAWINGS

The above objects and other advantages of the present invention willbecome more apparent by describing in detail preferred embodimentsthereof, with reference to the accompanying drawings, in which:

FIG. 1 a displays a cross-sectional view of the stator windings of atwo-pole, three-phase brushless dc motor.

FIG. 1 b displays one stator phase winding, represented by an electricside and an electric and magnetic side, of a two-pole, three-phasebrushless dc motor.

FIG. 1 c displays the electric and magnetic circuits of one stator phasewinding of a two-pole, three-phase brushless dc motor.

FIG. 1 d shows the magnetic and electric quantities of each phasevectorially along the positive magnetic axis for each stator phasewinding of a two-pole, three-phase brushless dc motor.

FIG. 1 e is a block diagram of the Brushless DC motor being driven by aDC brush motor as a prime mover to display the three phase generatedvoltages.

FIG. 2 a displays the three generated phase voltages;

FIG. 2 b displays the generated line voltages for a star connected BLDCmotor stator;

FIG. 2 c displays the supply line voltages for efficient motoroperation; and

FIG. 2 d displays the BEMF of the unenergized windings for the presentinvention.

FIG. 3 shows the phase windings of the BLDC motor connected in a stararrangement.

FIG. 4 a shows a schematic diagram of the electric and electric andmagnetic circuits of phase winding aa′ for the present invention,

FIG. 4 b shows the equivalent electric and magnetic circuits of phasewinding aa′ for the present invention,

FIG. 4 c shows a schematic diagram of the electric and electric andmagnetic circuits of phase winding aa′ and rotor magnet rotating for thepresent invention, while,

FIG. 4 d shows the equivalent electric and magnetic circuits of phasewinding aa′ and the effect of the rotating rotor magnet for the presentinvention.

FIG. 5 depicts the three-phase BLDC motor stator with magnetic andelectric quantities of each phase winding lying along their magneticaxis for the present invention.

FIG. 6 depicts a vector diagram of the flux vectors of each phasewinding, the resultant flux space vector of a pair of windings when themotor is energized with the line voltages of FIG. 2 c and the fluxvector of the rotor magnet for the present invention.

FIG. 7 depicts the electromagnetic torque waveform developed by themotor for one revolution of the rotor for the present invention.

FIG. 8 depicts a vector diagram of the trajectory of the BEMF SpaceVector for d-axis movement in the range 0°≦θ≦60° for the presentinvention.

FIG. 9 depicts a vector diagram of the trajectory of the BEMF SpaceVector for one complete rotation of the d-axis, that is, 0°≦θ≦360° forthe present invention.

FIG. 10 depicts a schematic diagram of the three-phase rectifier andinverter circuits used to power a motor and the equivalent circuit of aBLDC motor.

FIG. 11 depicts a schematic diagram of the equivalent circuit of BLDCmotor and the drive when transistors Q₁ and Q₂ are on thereby energizingwindings ac for d-axis of the motor in the range 0°≦θ≦60°.

FIG. 12 is a schematic diagram of the equivalent circuit of the BLDCmotor and drive when transistors Q₂ and Q₃ are on to energize windingsbc and winding aa′ is being commutated through anti-parallel diode D₄.

FIG. 13 is a vector diagram of the BEMF Space Vectors just before andafter commutation of current i_(a) in winding aa′ and the trajectoriesof the resultant voltage vector and the BEMF Space Vector under loadconditions for the present invention.

FIG. 14 shows a vector diagram of the trajectories of the resultantvoltage vector and the BEMF Space Vector under load conditions for onecomplete rotation of the rotor for the present invention.

FIG. 15 a shows the linear representation of an unskewed 2-polethree-phase BLDC motor showing only the center conductors of phasewinding aa′ for the present invention,

FIG. 15 b shows the linear representation of the same motor but havingthe rotor skewed by 20° for the present invention, while

FIG. 15 c shows the linear representation of the skewed rotor with theshift of the d-axis and the winding's magnetic axis by half the skewangle for the present invention.

FIG. 16 a depicts a cross sectional view of the unskewed rotor with thethree phase windings for the present invention,

FIG. 16 b shows an unskewed hexagonal trajectory of the BEMF SpaceVector for the present invention,

FIG. 16 c depicts a cross sectional view of the skewed rotor with thethree skewed phase windings for the present invention, and

FIG. 16 d shows a skewed hexagonal trajectory of the BEMF Space Vectorfor the present invention.

FIG. 17 shows the block schematic diagram of the drive used to implementthe present invention for efficient starting and commutation of athree-phase BLDC motor for the present invention.

FIG. 18 a shows the Parking routine for the present invention,

FIG. 18 b shows the calculation routine for the present invention,

FIG. 18 c shows Running routines for Windings_Count 1 and 2, for thepresent invention,

FIG. 18 d shows Running routines for Windings_Count 3 and 4 for thepresent invention and

FIG. 18 e shows Running routines for Windings_Count 5 and 6 for thepresent invention.

FIG. 19 a depicts the location of the positive magnetic axes for thethree phase windings of an unskewed rotor for the present invention,while,

FIG. 19 b shows the BEMF Space Vectors for winding commutation and thevalues of Ratio at the angles for winding commutation of an unskewedrotor for the present invention.

FIG. 20 a depicts the location of the positive magnetic axes for thethree phase windings of a skewed rotor for the present invention, while,

FIG. 20 b depicts the BEMF Space Vectors for winding commutation and thevalues of Ratio at the angles for winding commutation of a skewed rotorfor the present invention.

FIG. 21 a shows the Parking routine for the present invention,

FIG. 21 b shows the calculation routine for the present invention.

FIG. 21 c shows Running routines routines for Windings_Count 1 and 2 forthe present invention,

FIG. 21 d shows Running routines for Windings_Count 3 and 4 for thepresent invention, and

FIG. 21 e shows Running routines for Windings_Count 5 and 6 for thepresent invention.

FIG. 22 illustrates the techniques used in Running routines forWindings_Count 3 and 6, of FIG. 21 to ensure that commutation of phasewindings occur at the correct rotor position for the present invention.

DETAILED DESCRIPTION

The commutation technique employed in the present invention, overcomesall of the disadvantages of the known prior art, namely that of BEMFZero Crossing, BEMF Integration and the BEMF Third Harmonic SensorlessCommutation techniques. This said commutation technique of the presentinvention is sensorless and self-starting on load, thus making itsuperior to all known existing sensored and sensorless commutationtechniques. Additionally this said technique is used for starting andrunning the motor.

This said technique, utilises a Digital signal Processor (DSP) tocompute the stator phase voltage space vector, the rotation of which isdependent on the BEMF induced in the unenergized winding. As a result,this BEMF space vector sits on the rotor and provides rotor positioninformation as the rotor begins to move. It utilises the angle that theBEMF Space Vector makes with the real axis to commutate phase windingsand is easily applied to motors with any number of poles, provided thatthe rotor skew angle is known, thereby efficiently starting andcommutating a Brushless DC Motor.

With respect to the present invention, the production of a BEMF SpaceVector for starting and commutation of a Brushless DC Motor involves theknowledge of the phase BEMF waveforms as a function of rotor position,the production of magnetic axes of a three-phase stator, the developmentof an equivalent circuit of a phase winding containing electric andmagnetic quantities, the transformation of electrical variables unto themagnetic axis of a phase winding, to produce space representation ofvoltages and finally the addition of the three space phase voltagesvectorially to produce the BEMF Space Vector.

In addition, the effect of load current and skewing of the rotor toreduce cogging torque has an effect on the BEMF Space Vector and theseeffects must be taken into consideration when implementing the BEMFSpace Vector starting and commutation technique as articulated in thepresent invention.

A Brushless DC motor is operated by energizing two of its windings at atime. However, for efficient operation of the motor in a particulardirection of rotation, the pair of windings to be energized is dependenton the rotor position. This section determines the windings to beenergized for different rotor positions over a cycle of operation.

When a three-phase Brushless DC Motor (2) is driven by a prime mover,like a Brush DC Motor (1) at constant speed, the rotating rotor fluxinduces voltages in the phase windings. These voltage waveforms areobserved on an oscilloscope (3) using the resistor arrangement as shownin FIG. 1 e. These generated phase voltages from the oscilloscope areshown in FIG. 2 a. These generated phase voltages are trapezoidal innature, having flat tops of 120 electrical degrees and positive andnegative slopes each of 60 electrical degrees. Their magnitudes for aparticular Brushless DC Machine are dependent on the speed of rotation.The three generated phase voltages e_(an), e_(bn), and e_(cn), aredisplaced 120 electrical degrees from each other as shown in FIG. 2 a,and their variations are dependent on rotor position, since,

$e = {\frac{\lambda}{t} = {{\frac{\theta}{t} \cdot \frac{\lambda}{\theta}} = {\omega \frac{\lambda}{\theta}}}}$

where: e=generated voltage, λ=flux linkage, θ=rotor position andω=angular velocity of the rotor. From the above equation, the generatedvoltage waveform is a function of rotor position, thereby providing anindication of the rotor position at any time.

FIG. 2 a reveals that two phase voltages are of constant value for 60electrical degrees and for a star connected stator as shown in FIG. 3,line voltage waveforms can be drawn from the two phase voltages, whichare constant in value over a 60° internal. These line voltage waveformsare shown in FIG. 2 b.

Since two phase windings of a star connected Brushless DC motor areexperiencing a constant generated line voltage for 60 electricaldegrees, then efficient operation of the motor is obtained when the twoenergized windings are experiencing its constant BEMF. Hence, thegenerated line voltages shown in FIG. 2 b, which are functions of rotorposition are used to determine the sequence of energization of the motorwindings for a particular direction of rotation. Therefore using FIG. 2b, and starting with rotor position at θ=0°, the windings should beenergized ac, bc, ba, ca, cb, ab and ac again in that sequence, witheach pair of phase windings being energized for 60 electrical degrees.

FIG. 2 c shows the line voltages for efficient motor operation, placingthe supply voltages in phase with the generated or BEMF line values.

When the two phase windings are energized, and assuming that thepreviously energized winding loses the energy which was stored in itsmagnet field instantaneously when this winding was commutated, then thetwo energized windings would be experiencing half of the supply voltage,while the unenergized winding would be delivering its non constant BEMFduring this 60° internal. The BEMF of the unenergized winding is eitherfalling from its positive constant value to its negative constant valueor the reverse during this 60° interval. This changing BEMF of theunenergized windings shown in FIG. 2 d depicts the fundamental operatingprinciple of the present invention, which is utilised in starting andcommutating the Brushless DC motor of the present invention. Thetransformation of the two applied phase voltages of the conductingwindings and the BEMF of the unenergized phase winding from scalarquantities into vector quantities, involves vector analysis of thethree-phase stator.

Vector analysis of three-phase machines was first presented by Kovacsand Racz, later being detailed in a publication by Kovacs in 1984 andlays the foundation of vector analysis of three-phase machines. However,the approach and method of analysis lacks rigour in the production ofelectric current and supply voltage vectors.

The present invention by reduction to practice, utilises the concept ofvector analysis as presented by Kovacs and Racz to produce a model of astator winding, which includes electric and magnetic quantities, therebydemonstrating convincingly, that the magnitudes of electric scalar andmagnetic vector currents are equal.

This said equality of electric scalar and magnetic vector currents,would enable the referring of electric scalar voltages to the magneticaxis of the winding. Kirchhoff's voltage law would then be applied tothese spatial vector voltages to produce the supply voltage vector onthe magnetic axis of the winding. The application of the above resultsto a three-phase BLDC motor, would allow the supply phase voltagevectors of the two energized windings together with the BEMF vector ofthe unenergized winding, to be added vectorially to produce the BEMFSpace Vector for starting and commutating the BLDC motor.

A Brushless DC motor is wound with a three-phase stator. One phasewindings of a three-phase stator, showing only the center conducts ofphase winding aa′ and the rotor removed from the motor is shown in FIG.4 a. This phase winding possesses resistance, an electrical quantity andinductance, which is both an electrical and a magnetic quantity.Positive current i_(a) is shown entering winding aa′. The windingresistance R_(a) being an electrical quantity is removed from thewinding together with

${L_{a}\frac{i_{a}}{t}},$

which is an electrical voltage. These two quantities R_(a) and

$L_{a}\frac{i_{a}}{t}$

are placed in the electric circuit (6) with the supply voltage V_(an).

FIG. 4 b shows the equivalent electric and magnetic circuits joinedtogether but separated from each other by the dotted line. The electricscalar current i_(a), flows through the winding and produces vectormagnetic field intensity {right arrow over (H_(a))} along the positivemagnetic axis of winding aa′ (4) as shown in FIG. 4 a. The magnitude ofH_(a), is obtained by Amperes Circuital Law and is given by

$\frac{i_{a}l_{a}}{Na},$

where l_(a) is the length of the path of {right arrow over (H_(a))} andN_(a) is the number of turns of winding aa′. The magnetic fieldintensity {right arrow over (H_(a))} produces flux density {right arrowover (B_(a))}, which is co-linear with {right arrow over (H_(a))}, andwhich magnitude is given by μ|{right arrow over (H_(a)|)}, where μ isthe permeability of the medium through which {right arrow over (B_(a))}flows. Flux density {right arrow over (B_(a))} produces flux {rightarrow over (φ_(a))}, which is also co-linear with {right arrow over(B_(a))} and which magnitude is given by |{right arrow over(B_(a))}|A_(a) where A_(a) is the cross-sectional area of concern. Theflux linked with winding aa′ is given by {right arrow over (λ_(a))},which is co-linear with {right arrow over (φ_(a))} and which magnitudeis given by |{right arrow over (φ_(a))}|N_(a). And the flux linkage{right arrow over (λ_(a))} produces a current vector {right arrow over(i_(a))} which magnitude is given by

$\frac{\overset{->}{\lambda_{a}}}{L_{a}}$

which is co-linear with {right arrow over (λ_(a))}. Hence magneticquantities {right arrow over (H_(a))} {right arrow over (B_(a))}, {rightarrow over (φ_(a))}, {right arrow over (λ_(a))} and current vector{right arrow over (i_(a))} all lie along the positive magnetic axis aa′(4) and are spatial vector quantities possessing both magnitude anddirection.

Since current vector {right arrow over (i_(a))} leaves the magneticcircuit (7) of FIG. 4 b, a current vector {right arrow over (i_(a))}must also enter the series connected magnetic circuit (7). In addition,since the electric and magnetic circuits are connected in series, thisimplies that the scalar electric current i_(a) is of same magnitude asthe vector magnetic current {right arrow over (i_(a))}. The separationof electric and magnetic circuits is shown by the dotted vertical line,with the magnetic current vector {right arrow over (i_(a))} taking up ascalar value when it enters the electric circuit (6) and the scalarelectric current i_(a) taking up a vector magnetic value when it entersthe magnetic circuit (7) as shown in FIG. 4 b. Hence the magnetic axisof winding aa′ completes the electric circuit making {right arrow over(i_(a))} and |{right arrow over (i_(a))}| of same magnitude.

If i_(a) is changing, then the effect of the magnetic circuit on theelectric circuit is seen in the voltage

$L_{a}\frac{i_{a}}{t}$

which opposes the current i_(a). Since the magnitude of i_(a) and {rightarrow over (i_(a))} are equal and {right arrow over (i_(a))} lies alongthe winding's magnetic axis, then the voltages i_(a)R_(a) and

$L_{a}\frac{i_{a}}{t}$

can be referred to the magnetic axis of winding aa′ without changingtheir magnitudes. The vector summation of {right arrow over (i_(a))}R_(a) and

$L_{a}\frac{\overset{\rightarrow}{i_{a}}}{t}$

along the magnetic axis of winding aa′, produces the supply voltagevector {right arrow over (V_(an))} along the magnetic axis of windingaa′.

When the rotor (10) is inserted in the motor as shown in FIG. 4 c andthe motor is running, the generated voltage vector or BEMF vector inwinding aa′ is given by {right arrow over (e_(an))} where

$\overset{\rightarrow}{e_{an}} = \frac{\overset{\rightarrow}{\lambda_{{maa}^{\prime}}}}{t}$

and {right arrow over (λ_(maa′))}, is the flux linkage vector producedby the rotor magnet flux vector {right arrow over (φ_(m))} on windingaa′ as shown in FIG. 4 d. This BEMF vector {right arrow over (e_(an))}existing on the magnetic axis of FIG. 4 d is converted to the scalarBEMF e_(an) on the electric side of by the BEMF Vector to ScalarConverter block of FIG. 4 d. The magnetic quantities which are producedby the vector current {right arrow over (i_(a))} are given by {rightarrow over (H_(ai))} {right arrow over (B_(ai))}, {right arrow over(φ_(ai))} and {right arrow over (λ_(ai))} in FIG. 4 d.

Applying Kirchhoff's voltage law to the electric and magnetic sides ofFIG. 4 d yields,

$V_{an} = {{i_{a}R_{a}} + {L_{a}\frac{i_{a}}{t}} + {e_{an}\mspace{14mu} {for}\mspace{14mu} {the}\mspace{14mu} {electric}\mspace{14mu} {side}}}$and$\overset{->}{V_{an}} = {{\overset{->}{i_{a}}R_{a}} + {L_{a}\frac{\overset{->}{i_{a}}}{t}} + {\overset{->}{e_{an}}\mspace{14mu} {for}\mspace{14mu} {the}\mspace{14mu} {magnetic}\mspace{14mu} {{side}.}}}$

The method as heretofore outlined, allows the magnetic and electricalquantities of a stator winding in a Brushless DC motor to be representedvectorially along the winding's magnetic axis. When this technique isapplied to the three phases of a three-phase, two-pole Brushless DCmotor, which phase windings are displaced from each other by 120electrical degrees, the magnetic and electric quantities of each phasecan be represented vectorially along the positive magnetic axis forphase winding aa′ (4), positive magnetic axis for phase winding bb′ (8)and positive magnetic axis for phase winding cc′ (9) as shown in FIG. 5.

Having proven that all electric phase voltage quantities can berepresented along the magnetic axis of a plane winding, the magneticproperties of the three-phase stator of a Brushless DC motor, due toenergization of two phase windings in a particular sequence, will bedeveloped to allow the torque production mechanism of the Brushless DCmotor to be presented.

FIG. 6 contains a three-phase stator (5) of a 2-pole Brushless DC motor,showing the center conductors of each phase winding and the positivemagnetic axis for phase winding aa′ (4), positive magnetic axis forphase winding bb′ (8) and positive magnetic axis for phase winding cc′(9). The magnetic properties of each phase winding is determined whenthe star connected stator is energized in the sequence ac, bc, ba, ca,cb and ab to complete one cycle of energization. The first letter in awinding pair, indicates that current enters that phase winding at thatlettered terminal and the last letter indicate that current leaves thatphase winding at that lettered terminal. These winding terminals areshown in FIG. 3. Energization of the stator windings in the sequence ac,bc, ba, ca, cb and ab produces stator flux vectors {right arrow over(φ_(ac))}, {right arrow over (φ_(bc))}, {right arrow over (φ_(ba))},{right arrow over (φ_(ca))}, {right arrow over (φ_(cb))}, and {rightarrow over (φ_(ab))} respectively.

These stator flux vectors are all of equal magnitude and occupy a fixedposition in the stator. The stationery stator flux vectors are displacedfrom each other by an angle of 60 electrical degrees and theirmagnitudes are dependent on the current flowing in the phase windings.If the 2-pole rotor magnet (10) is assumed to be moving at a constantangular velocity ωin an anticlockwise direction, then, at the instant ofobservation in FIG. 6, it's d-axis (12) which is defined as the centerof the south pole is at θ=0°.

At this rotor position θ=0°, windings ac would begin to experience itsconstant BEMF due to the effect of the rotor magnet on the statorwindings. The energization of windings ac produces the stationary statorflux vector {right arrow over (φ_(ac))}. Since {right arrow over(φ_(ac))} and all the other stationary stator flux vectors are enteringthe stator body, they are described as producing south poles of anelectromagnet. The rotor magnet has its flux leaving the north pole andentering the south pole. Representing the rotor flux vector as {rightarrow over (φ_(m))}, then the interaction of {right arrow over (φ_(m))}with {right arrow over (φ_(ac))} develops torque to produce rotorrotation in an anticlockwise direction. The electromagnetic torquedeveloped by the interaction of these flux vectors is given by thevector cross product by Vas,

{right arrow over (Te)}=C{right arrow over (φ_(m))}×{right arrow over(φ_(ac))}

{right arrow over (Te)}=C|{right arrow over (φ_(m))}∥{right arrow over(φ_(ac))}| Sin α{right arrow over (k)}

where {right arrow over (Te)} is the electromagnetic torque developed bythe motor, α is the angle between flux vectors {right arrow over(φ_(m))} and {right arrow over (φ_(ac))}, C is a constant and {rightarrow over (k)} is the unit vector whose direction is perpendicular tothe plane in which {right arrow over (φ_(m))} and {right arrow over(φ_(ac))} exists.

As the motor rotates from its initial position θ=0° in an anticlockwisedirection that is for θ increasing (11), the angle α decreases from120°, thereby increasing the electromagnetic torque developed by themotor. When a α=90°, the developed torque is maximum, but as α reaches60°, it decreases to the value when θ was 0°. When θ>60° or α<60° theBEMF in windings ac is no longer at its constant value for this speed ofoperation as shown in FIGS. 2 a-2 d, and the electromagnetic torquedeveloped would be less than the values obtained for 60° a 120°.

Hence, winding aa′ must be commutated and winding bb′ must be broughtinto conduction with winding cc′. That is, windings be must be energizedat θ=60°. The same process of torque production continues until θ=120°and a new pair of windings ba is brought into conduction. Theelectromagnetic torque developed by the machine is not constant througheach 60° movement of the rotor and is given by

{right arrow over (T_(e))}=m Sin α{right arrow over (k)}

where m=C|{right arrow over (φ_(m))}∥{right arrow over (φ_(ac))}| and60°≦α120°. The electromagnetic torque developed by the motor for onerevolution of the rotor is depicted in FIG. 7.

The heretofore described events are for efficient operation in thethree-phase Brushless DC motor showing the range of rotor positions fora pair of windings to remain energized and the corresponding BEMF of thegiven energized windings and the torque developed are summarised inTable 1.

TABLE 1 Windings Rotor Position Constant Electromagnetic TorqueEnergized Range BEMF Developed 60° ≦ α ≦ 120° ac  0 ≦ θ ≦ 60° E_(ac)mSinα bc  60 ≦ θ ≦ 120 E_(bc) mSinα ba 120 ≦ θ ≦ 180 E_(ba) mSinα ca 180≦ θ ≦ 240 E_(ca) mSinα cb 240 ≦ θ ≦ 300 E_(cb) mSinα ab 300 ≦ θ ≦ 360E_(ab) mSinα

Having described the torque production mechanism of the motor as itrelates to rotor position and windings energization, the technique ofthe present invention will now be described to commutate phase windingsand produce the required sequence of energization for efficient motoroperation.

In order to provide an efficient energy conversion process in theconversion of electrical energy into mechanical energy through thedevelopment of electromagnetic torque, the rotor position must be knownto ensure that the two phase windings are energized at the correctinstant. The BEMF Space Vector is obtained by vectorially summing thephase voltage vectors of the energized windings with the BEMF vector ofthe unenergized winding.

If the three-phase Brushless DC motor is being commutated for efficientoperation and running at constant speed ω the supply and BEMF waveformsare shown in FIGS. 2 a-2 d. Since the phase applied voltage vectors andBEMF vector lie on the phase magnetic axes and the axes are displaced120 electrical degrees from each other as shown in FIG. 5, the phasevoltage vectors can be added vectorially to produce a BEMF Space Vector{right arrow over (V_(R))} where,

{right arrow over (V _(R))}={right arrow over (V _(an))}+{right arrowover (V _(bn))}+{right arrow over (V _(cn))}

where {right arrow over (V_(an))}, {right arrow over (V_(bn))} and{right arrow over (V_(cn))} represent the voltage vectors of windingsaa′, bb′ and cc′ respectively and lie along their magnetic axes and

{right arrow over (V _(R)=)}v_(an) e ^(j0) °+v _(bn) e ^(j120) °+v _(cn)e ^(j240°)

where v_(an), v_(bn) and v_(cn) represents the instantaneous voltages ofphase windings aa′, bb′ and cc′ respectively and e^(j0)°, e^(j120)° ande^(j240)° represents the position of the positive magnet axes ofwindings aa′, bb′ and cc′ respectively. Considering no-load conditionsand starting with the d-axis at rotor position θ=0°, windings ac areenergized with the supply voltage V. Assuming commutation of the currentin the previous phase winding is completed, then

${V_{an} = \frac{V}{2}},{V_{nc} = {{\frac{V}{2}\therefore V_{cn}} = {- {\frac{V}{2}.}}}}$

Representing the constant phase BEMF as E and the varying phase BEMF ase; then for motor operation

$\frac{V}{2} > {E.}$

But under no-load conditions

${\frac{V}{2} \approx E},$

since the line currents are small. With the d-axis at θ=0° using thewaveforms of FIGS. 2 a-2 d:

$v_{bn} = {{{{- E} \approx {- \frac{V}{2}}}\therefore\overset{->}{V_{R\; 1}}} = {{\frac{V}{2} - {\frac{V}{2}^{j\; 120^{\circ}}} - {\frac{V}{2}^{j\; 240^{\circ}}}} = {V\; ^{j\; 0^{\circ}}}}}$

where {right arrow over (V_(R1))} is the BEMF Space Vector at θ=0°.

It must be noted from FIG. 6 that the d-axis (12) position at θ=0° leadsthe real positive axis by 90°. With the d-axis at θ=30° and using thewaveforms of FIGS. 2 a-2 d,

${V_{an} = \frac{V}{2}},{V_{bn} = 0},{V_{cn} = {- \frac{V}{2}}}$$\overset{->}{V_{R\; 1\_ \; 2}} = {{\frac{V}{2} - {\frac{V}{2}^{j\; 240^{\circ}}}} = {0.866\; ^{j\; 30^{\circ}}}}$

where {right arrow over (V_(R1) _(—) ₂)} is the BEMF Space Vector atrotor position θ=30° and for rotor position θ=60°, the waveforms ofFIGS. 2 a-2 d reveals

${V_{an} = \frac{V}{2}},{V_{bn} = {E \approx \frac{V}{2}}},{V_{cn} = {- \frac{V}{2}}}$$\overset{->}{V_{R\; 2}} = {{\frac{V}{2} + {\frac{V}{2}^{j\; 120^{\circ}}} - {\frac{V}{2}^{j\; 240^{\circ}}}} = {V\; ^{j\; 60^{\circ}}}}$

When the d-axis (12) of the rotor is at position θ=0°, 30° and 60°, theBEMF Space Vector {right arrow over (V_(R))} is at e^(j0)° e^(j30)° ande^(j90)° respectively as shown in FIG. 8. For d-axis (12) at θ=0° and60° in FIG. 8, the BEMF Space Vector is of magnitude V and at θ=30°, theBEMF Space Vector magnitude is 0.866V. Hence, the trajectory of the BEMFSpace Vector for the sector (13) for θ increasing (11) in the range0°≦θ≦60° is along the base of a triangle whose adjacent sides are givenby the BEMF Space Vectors at θ=0° and θ=60° as shown in FIG. 8.

It is observed in FIG. 8 that the BEMF Space Vector {right arrow over(V_(R))} follows the d-axis of the rotor magnet and lags it by 90electrical degrees. This ability of the BEMF Space Vector to follow thed-axis of the rotor is due to the fact that the BEMF of the unenergizedwinding is employed in the determination of the BEMF Space Vector andthis BEMF is a function of rotor position, since for unenergized windingbb′,

$e_{bn} = {\frac{\lambda_{{mbb}^{\prime}}}{t} = {{\frac{\lambda_{{mbb}^{\prime}}}{\theta} \cdot \frac{\theta}{t}} = {\omega \frac{\lambda_{{mbb}^{\prime}}}{\theta}}}}$

and hence e_(bn), is a function of θ. Hence, the BEMF Space Vector{right arrow over (V_(R))} is fixed to the rotor provided rotor is notat standstill. Therefore, this BEMF Space Vector possesses rotorposition information, and lags the d-axis of the rotor magnet by 90electrical degrees. The angle made by the BEMF Space Vector with thereal axis provides rotor position information in this invention.

Since a new pair of windings are energized by the dc supply for every 60electrical degree movement of the d-axis from its starting point atθ=0°, then for every 60 electrical degree movement of the BEMF SpaceVector from its starting position at e^(j0)°, a new pair of windings areenergized by the dc bus. The magnitude and location of the BEMF SpaceVector for every 60 electrical degrees movement of the rotor's d-axisstarting at θ=0°, together with the new pair of windings to be energizedfor these angles are shown in Table 2.

TABLE 2 Position of BEMF New Windings d-axis θ Space Vector Energised 0° {right arrow over (V_(R1))} = Ve^(j0°) ac  60° {right arrow over(V_(R2))} = Ve^(j60°) bc 120° {right arrow over (V_(R3))} = Ve^(j120°)ba 180° {right arrow over (V_(R4))} = Ve^(j180°) ca 240° {right arrowover (V_(R5))} = Ve^(j240°) cb 300° {right arrow over (V_(R6))} =Ve^(j300°) ab 360° {right arrow over (V_(R1))} = Ve^(j360°) ac

A plot of the BEMF Space Vector for 0≦θ≦360° has a trajectory of ahexagon as shown in FIG. 9. Also included in FIG. 9 are the stationaryflux vectors obtained by energizing two windings in the sequence foranticlockwise rotation of rotor and the positive magnetic axes for eachphase winding. FIG. 9 shows that as the rotor rotates at a constantangular velocity ω rad/s, the BEMF Space Vector {right arrow over(V_(R))} rotates with the same angular velocity ω rad/s but lags therotor's d-axis by 90 electrical degrees. The trajectory of the BEMFSpace Vector (21) is a hexagon as shown in FIG. 9.

In this invention, the commutation of phase windings and the connectionof the pair of windings to the supply for efficient operation of themotor are accomplished with the use of the said BEMF Space Vector. Whenthe BEMF Space Vector reaches the real positive axis, {right arrow over(V_(R))}={right arrow over (V_(R1))}=Ve^(j0)° as shown in FIG. 9. Atthis position of the BEMF Space Vector, the d-axis of the rotor magnetis at θ=0°. At this angle of θ, the phase winding bb′ must be commutatedand the windings ac must be connected to the supply voltage. When theBEMF Space Vector reaches {right arrow over (V_(R2))}=Ve^(j60)°, phasewinding aa′ is commutated and the new winding pair be is connected tothe supply voltage. For efficient motor operation, the locations of theBEMF Space Vector shown in Table 2 are used to commutate a phase windingand apply a pair of phase windings to the dc supply.

Although the BEMF Space Vector possesses magnitude and direction, it isonly the angle that this space vector makes with the real axis and notits magnitude which is used to commutate a phase winding and ensure thatthe correct pair of windings is energized for efficient operation of theBrushless DC motor. Hence, the magnitude of the BEMF which isproportional to the speed of motor operation is not directly utilised inthe present invention, but the angle that this BEMF Space Vector makeswith the real axis or its resolver information is used in thisinvention.

The self-starting ability of the present invention together withensuring that motor operation is in one direction only on starting;thereby eliminating backward rotation of the motor will now beaddressed. To ensure motor operation in one direction only when themotor is started from rest, the motor must first be parked along one ofthe stationary stator flux vectors shown in FIG. 9. Parking the rotor'sd-axis at θ=0° or the north pole of the rotor magnet along thestationary stator flux vector {right arrow over (φ_(cb))} isaccomplished by energizing windings cb in FIG. 9. When windings cb areenergized, electromagnetic torque is developed due to the interaction ofrotor flux vector {right arrow over (φ_(m))} and stationary stator fluxvector {right arrow over (φ_(cb))} shown in FIG. 9. This electromagnetictorque pulls the rotor flux vector {right arrow over (φ_(m))} intoalignment with {right arrow over (θ_(cb))}, thereby aligning the d-axisof the rotor, the south pole of the rotor magnet, to the θ=0° position.

After a short time interval when the rotor has settled in the θ=0°position, the motor is started from standstill in an anticlockwisedirection by energizing phase windings ac. The parking of the rotor'sd-axis at θ=0° and energization of windings ac ensures onlyanticlockwise forward rotation by the motor on starting and eliminatesany possible backward rotation of the motor in the starting process.With windings ac energized at θ=0°, the starting electromagnet torquedeveloped by the motor is given by

{right arrow over (T _(e))}=C{right arrow over (φ_(m))}×{right arrowover (φ_(ac))}.

The magnitude of {right arrow over (φ_(ac))} is dependent on the windingcurrents, which in turn depends on the supply voltage and BEMF of thephase windings. At standstill, the BEMF generated in the windings iszero and the windings currents are high enough to developelectromagnetic torque to overcome friction, inertia and any loadtorques; which oppose the electromagnetic torque. The torque equation isgiven by:

T _(e) =T _(I) +T _(F) +T _(L)

where T_(I) is the inertia torque, T_(F) is the friction torque andT_(L) is the load torque. As the rotor accelerates from rest, the statorwindings develop BEMFs due to rotation of the rotor magnetic field. TheBEMFs generated in the energized windings decreases the windingcurrents, which in turn decreases the magnitude of the stationary statorflux vector {right arrow over (φ_(ac))}; thus decreasing theelectromagnetic torque developed by the motor.

The resultant voltage vector at the instant of starting is produced bythe phase voltage vectors of the energized windings alone, since theBEMF of the unenergized winding is zero at starting. This resultantvoltage vector {right arrow over (V_(R))} is stationary and of constantmagnitude. However, it is the BEMF vector in the unenergized phasewinding bb′, which is non-zero and varying when the motor starts toturn, as a result of the electromagnetic torque developed on startingwhich when added to the stationary phase voltage vectors of theenergized windings, produces the BEMF Space Vector.

The BEMF e_(b) on phase winding bb′ is zero at θ=0° and as θ increases,e_(b) goes negative and then goes through a zero crossing, then goespositive in value to its constant value

$E \approx \frac{V}{2}$

as shown in FIG. 2 a. This variation of e_(b) causes the BEMF SpaceVector {right arrow over (V_(R))} to start along the {right arrow over(φ_(ac))} stationary flux vector at e^(j30°), then, rotate backwardsbefore rotating in the forward anticlockwise direction. When e_(b) is atit's zero crossing, {right arrow over (V_(R))} is again at the positione^(j30)°, when

${e_{b} = {E \approx \frac{V}{2}}},$

{right arrow over (V_(R))} is at the e^(j60°) position and phase windingaa′ must be commutated and winding be connected to the supply. The rotorcontinues to develop torque for θ is now 60° and {right arrow over(φ_(m))} interacts with {right arrow over (φ_(bc))} in the torqueproduction process.

The six angles of the BEMF Space Vector in Table 2 are used to connectnew windings to the supply thus sustaining rotation and bringing themotor up to steady—state speed for the supply voltage of V. Thisself-starting ability of the present invention separates it from all ofthe other sensorless techniques used for the commutation of Brushless DCmotors. The self-same technique used to commutate windings insteady-state operation of the present invention is used to start themotor from rest under no-load and load conditions.

In order to connect two-phase windings to the dc supply and change thewinding pair to achieve efficient operation of the Brushless DC motor,the circuit shown in FIG. 10 is used. It consists of a three-phasebridge rectifier (15) consisting of diodes D₇ through D₁₂ supplied by athree-phase voltage supply (14), a filter Capacitor C₁ to supply the DCbus voltage V, and six insulated-gate bipolar transistors (IGBTs)forming a three-phase H-bridge inverter and consisting of transistors Q₁through Q₆ and their anti-parallel diodes D₁ through D₆. An electricalmodel of the Brushless DC motor with its three phase winding aa′, bb′and cc′ is also presented. Table 3 shows the transistors to be turned onfor motor operation in an anticlockwise direction. The BEMF Space Vectordetermined earlier reflected motor operation on no-load when the windingcurrents were small in comparison to full load currents. Under theseno-load conditions, the current in the winding which is being commutatedis small and decays very quickly through one of the transistoranti-parallel diodes as depicted in FIG. 10.

TABLE 3 BEMF Space Windings to Transitions to Vector Angle be Energisedbe turned on  0° ac Q₁ and Q₂  60° bc Q₂ and Q₃ 120° ba Q₃ and Q₄ 180°ca Q₄ and Q₅ 240° cb Q₅ and Q₆ 300° ab Q₆ and Q₁ 360° or 0° ac Q₁ and Q₂

Under load conditions, the winding currents are high and take some timeto decay in the winding being commutated, thus providing new commutationissues. The effect of these commutation issues on motor and driveoperation and on the BEMF Space Vector will now be addressed. The motoris loaded and assumed to be running at a constant speed.

The d-axis of the rotor magnet is in the range 0°<θ<60° and under theseconditions windings ac are energised through transitions Q₁ and Q₂. Inthe interval of analysis, the motor current is assumed to be constantand two phase windings are connected to the dc supply. The motor anddrive equivalent circuit under these given conditions are shown in FIG.11.

Taking,

E_(an)=E_(bn)=E_(cn)=E

R_(a)=R_(b)=R_(c)=R

L_(a)=L_(b)=L_(c)=L

for a 160V trapezoidal BEMF Brushless DC motor, of full-load current 4Aand phase resistance 1Ω, then under steady-state conditions for thecircuit in FIG. 11,

V=2Ri _(a)+2E.

Since for 0°<θ<60°, E_(an)=−E_(cn) as shown in FIG. 2, therefore, E=76Volts, which is 95% of V/2. Hence, under no-load, full load and allother load conditions, the steady BEMF of each phase winding would beassumed equal to half the supply voltage.

When θ=60°, the BEMF Space Vector is given by Ve^(j60)°. For efficientmotor operation, winding aa′ must be commutated and windings bc must beconnected to the supply at this rotor position. The current in phasewinding aa′ would take some time to decay to zero, since a large amountof energy was stored in the winding magnetic field and this energy mustbe dissipated. The release of this magnetic field energy from windingaa′ tries to maintain the current in the winding, thus causing windingaa′ to take some time to commutate its current. The equivalent circuitof motor and drive when windings bc are energized and phase winding aa′is being commutated is depicted in FIG. 12.

The energy released from winding aa′, develops the voltage

$L_{a}\frac{i_{a}}{t}$

to maintain the flow of i_(a) through anti-parallel diode D₄ andtransistor Q₂. The current i_(a) flows against BEMFs e_(an) and E_(nc)and winding resistances R_(a) and R_(c) and also against

$L_{c}\frac{i_{c}}{t}$

if current i_(c) is increasing. The current i_(a) in winding aa′ iscommutated when

$L_{a}\frac{i_{a}}{t}$

is less than the sum of e_(an) plus E_(nc) and

$L_{c}{\frac{i_{c}}{t}.}$

Under these conditions, the phase voltages across the windings are givenby:

${V_{an} = {- \frac{V}{3}}},{V_{bn} = {{\frac{2V}{3}\mspace{14mu} {and}\mspace{14mu} V_{cn}} = {- \frac{V}{3}}}}$

and the resultant voltage vector during this commutation interval isgiven by V {right arrow over (_(Rcaa′))}, where

{right arrow over (V _(RCaa′))}={right arrow over (V _(an))}+{rightarrow over (V _(bn))}+{right arrow over (V _(cn))}

and

{right arrow over (V_(Rcaa′))}=Ve^(j120)°.

The above equation reveals that the resultant voltage vector duringcommutation of current i_(a) in winding aa is a stationary vector ofmagnitude V and located at a position e^(j120)°. The d-axis of the rotormagnet and the BEMF Space Vector just at the point before the beginningof the commutation internal of current i_(a) in winding aa were locatedat θ=60° and e^(j60)° respectively, thus allowing the BEMF Space Vectorto lag the d-axis by 90 electrical degrees. However, during thecommutation internal of circuit i_(a), the resultant voltage vector{right arrow over (V_(Rcaa′))} takes up a stationary position ate^(j120)°, although the rotor is moving during this interval, taking upangles of θ>60°. It must be noted, that the resultant voltage vectorduring commutates of i_(a) has no BEMF associated with it and unlike theBEMF Space Vector, it does not reflect rotor position information.Hence, the angles that this resultant voltage vector makes with the realaxis should not be used to commutate winding currents.

When the current i_(a) in winding aa′ has been commutated, the BEMF inthis winding is no longer V/2, but much less than this, say 0.4V. Thephase voltages at this instant are given by

${V_{an} = {0.4V}},{V_{bn} = {{\frac{V}{2}\mspace{14mu} {and}\mspace{14mu} V_{cn}} = {- \frac{V}{2}}}},$

and the BEMF Space Vector at the end of the commutation interval ofwinding aa is given by {right arrow over (V_(Rcaa′) _(—) _(E))}, where,

{right arrow over (V_(Rcaa′) ^(—) _(E))}=0.9549Ve^(j65)°.

This BEMF Space Vector, having the BEMF of phase winding aa possessesrotor position information and follows the d-axis of the rotor magnet,lagging it by 90 electrical degrees. The BEMF Space Vectors just beforecommutation of winding aa′ (16) and the BEMF Space Vectors just aftercommutation of winding aa′ (17) and the resultant voltage vectortrajectory during commutation of i_(a) are shown in FIG. 13.

The trajectory of the BEMF Space Vector (21), the resultant voltagevector during commutation (18), the trajectory of the resultant voltagevector at the beginning of commutation (19) and the trajectory of theresultant voltage vector at the end of commutation (20), are shown inFIG. 13. It must be noted that as the motor load increases, the phasecurrents increase and the time to commutate a winding current increases,hence the angles formed by the BEMF Space Vector just before and justafter commutation of a phase winding increases with the increase of loadcurrent. For one complete electrical cycle of operation, thetrajectories of the BEMF Space Vector and the resultant voltage vectorduring commutation are shown in FIG. 14. At rotor position θ=0° in FIG.14, the BEMF Space Vector {right arrow over (V_(R1))} (22) is producedfor the commutation of phase winding bb′ and the connection of the newwindings ac situated at the {right arrow over (V_(R1))} vertex of thehexagon (25). Resultant stationary stator flux vector {right arrow over(φ_(ac))} (24) produced by this energization would interact with rotorflux vector {right arrow over (φ_(m))} (23) to develop electromagnetictorque. The trajectory of the resultant voltage vector at the beginningof commutation (19), trajectory of the resultant voltage vector at theend of commutation (20) and the trajectory of the BEMF Space Vector (21)are also presented.

Rotor magnets are skewed to reduce the cogging torque experienced by therotors. However, the skewing of the rotor magnet of a Brushless DC motoraffects the orientation of the trajectory of the BEMF Space Vectorproduced by the motor. The effect of the skewed rotor on the magneticaxes of a Brushless DC motor is presented in FIGS. 15 a-15 c. The linearrepresentation of an unskewed 2-pole, three-phase Brushless DC motorshowing only the center conductors of phase windings aa′ is presented inFIG. 15 a. The unskewed rotor is positioned in the diagram with itsd-axis aligned with conductor of winding aa′. This represents the θ=0°position of the rotor. At this rotor position the unskewed line xy,separating north and south magnetic pole pieces is aligned with themagnetic axis of winding aa′. With rotor movement (30) in the directionshown, the flux linkage of winding aa′ at the position shown in FIG. 15a is zero, since the winding is experiencing equal flux from both northand south poles of the magnet. As a result, the induced emf or BEMF ofthis winding is zero in the position shown and lies along the magneticaxis of winding aa′.

FIG. 15 b shows a skewed rotor magnet, with skew angle of β=20°. Forthis skewed magnet, the line xy separating north and south magnetic polepieces is sloped at an angle of β to the vertical. The skewing of therotor causes the d-axis, which is the center of the south-pole, to shiftby β/2=10° (31) to the right in the direction of skew, as shown in FIG.15 b. When this rotor magnet is moving in the direction shown, the fluxlinkage in winding aa′ is not zero at the rotor position of FIG. 15 b,since the winding is experiencing more flux from the south magnetic polethan from the north magnetic pole. As a result, a BEMF is induced inwinding aa′.

For this rotor position of FIG. 15 b to produce a net flux linkage ofzero in winding aa′, resulting in zero BEMF in the winding, therebyensuring that the BEMF of the skewed and unskewed rotors are in phase,winding aa′ must be shifted towards the right by an angle β/2=10° asshown in FIG. 15 c. This shift of winding aa′ by β/2, causes themagnetic axis of winding aa′ to be shifted by β/2=10° (32) and in thesame direction in which the d-axis was shifted due to skewing of themagnet.

The effect of the skewed rotor on the d-axis of the rotor magnet and themagnetic axes of all three phase windings are shown in FIGS. 16 a-16 d.The stator and unskewed rotor (26) of a 2-pole, three-phase Brushless DCmotor, indicating only the center conductors of each phase winding isshown in FIG. 16 a. Since phase winding positive magnetic axes aa′, bb′and cc′ are positioned at e^(j0)°, e^(j120)° and e^(j240)° respectively,the trajectory of the BEMF Space Vector is an unskewed hexagon (28)whose BEMF Space Vectors {right arrow over (V_(R1))} through {rightarrow over (V_(R6))} which are used for commutation of phase windingswith the present invention all lie along the lines from the center tothe vertices of the hexagon, where these lines have the same directionas the magnetic axes of the phase windings as shown in FIG. 16 b.

The skewed rotor (27), with its d-axis shifted by β/2=10° in a clockwisedirection relative to the unskewed rotor is shown in FIG. 16( c)together with the center conductors of the three stator windings. Thephase windings together with their magnetic axes are also shifted byβ/2=10° to ensure that the BEMFs in the skewed and unskewed rotors arein phase with each other. This ensures that at the θ=0° position, thed-axis is 90° away from the positive magnetic axis of winding aa′ forboth skewed and unskewed rotors. Since the vector phase voltages liealong the magnetic axes of the windings and the new positions of theseaxes for the skewed rotor are e^(j−10)°, e^(j110)° and e^(j230°), forwindings aa′, bb′ and cc′ respectively, then the trajectory of the BEMFSpace Vector is a skewed hexagon (29) as shown in FIG. 16 d.

The effect of rotor skew is to shift the BEMF Space Vectors {right arrowover (V_(R1))} through {right arrow over (V_(R6))} which are used tocommutate phase windings by an angle β/2=10° in a clockwise direction.Hence, the rotor skew angle must be known in order to produce the skewedhexagon whose BEMF Space Vectors {right arrow over (V_(R1))} through{right arrow over (V_(R6))} are used in the present invention forefficient starting and running of the Brushless DC motor. Table 4summarises d-axis position and BEMF Space Vector for new winding pairfor skewed rotor of β=20°.

TABLE 4 Position of BEMF New Windings d-axis θ Space Vector Energised 0° {right arrow over (V_(R1))} = Ve^(−j10°) ac  60° {right arrow over(V_(R2))} = Ve^(j50°) bc 120° {right arrow over (V_(R3))} = Ve^(j110°)ba 180° {right arrow over (V_(R4))} = Ve^(j170°) ca 240° {right arrowover (V_(R5))} = Ve^(j230°) cb 300° {right arrow over (V_(R6))} =Ve^(j290°) ab 360° {right arrow over (V_(R1))} = Ve^(−j10°) ac

INDUSTRIAL APPLICABILITY

The block diagram of the drive used for the implementation of the DeFour BEMF Space Vector Resolver for efficient starting and commutatingthe three-phase Brushless DC motor is shown in FIG. 17. It consists of aprogrammed Digital Signal Processing Means (33), a Digital SignalProcessor (DSP) Board (35), an Isolation & Driver Circuit (40), athree-phase Inverter Circuit (45), a Brushless DC Motor (47), a PhaseVoltage Sensing Circuit (51) and a Phase Voltage Isolation Circuit (48).The programmed Digital Signal Processing Means (33) is used to downloadthe machine language program to the Analog Devices ADMC 401 DSP board(35) via the serial communication cable (34). The DSP runs the presentinvention's program and provides the information necessary to drive twoof the six transistors in the three-phase Inverter Circuit (45) at anyinstant of time, by way of the six output lines a⁺, a⁻, b⁺, b⁻, c⁺ andc⁻ (36). The six output lines of the DSP Board are used to drive six6N136 optocouplers (37) which isolates the DSP Board from the levelshifting section of the Isolation & Driver Circuit (40). The sixisolated lines, a_(i) ⁺, b_(i) ⁺, b_(i) ⁻, c_(i) ⁺ and c_(i) ⁻ (38) fromthe optocouplers are fed to the level shifter and driver section (39) ofthe Isolation & Driver Circuit (40). The IR2133 integrated circuit wasused as the level shifter and driver. Level shifting is necessarybetween the DSP Board and the insulated gate bipolar transistors (IGBTs)of the three-phase Inverter Circuit (45), to shift the 5V level DSPsignals to a 15V level for driving the IGBTs.

The IRPT2056A was used to supply the dc power through its three-phaserectifier and the three-phase inverter stage with its six IGBTs Q₁ to Q₆and their anti-parallel diodes D₁ to D₆ was used to supply this DC powerto the Brushless DC motor. Isolated and level shifted DSP signals a_(il)⁺ and a_(il) ⁻ drive the transistors Q₁ and Q₄ in leg-a (42), b_(il) ⁺and b_(il) ⁻ drive transistors Q₃ and Q₆ in leg-b (43) and c_(il) ⁺ andc_(il) ⁻ drive the transistors Q₂ and Q₅ in leg-c (44) of the invertercircuit. These IGBTs are driven fully on or off, with only twotransistors on at any one time, one on the high side which is connectedto the positive dc supply and one on the low side which is connected tothe negative dc supply.

The three phase winding lines (46) of the Brushless DC motor areconnected to the emitter-collector nodes of the transistors in eachinverter leg. Since the present invention utilises motor phase voltagesand the star point of the phase windings is not accessible, the resistornetwork formed by R₁ and R₂ of the Phase Voltage Sensing Circuit (51)provides this star point at termination n of the three lower resistorsR₂. The six resistors comprising the Phase Voltage Sensing Circuit (51)was used to provide a fraction of the motor phase voltage of magnitude<3V to feed the analog to digital converter (A/D) of the DSP (35).

Before going to the DSP (35), the sampled phase voltages produced by thePhase Voltage Sensing Circuit (51) must be isolated from the power linereference by the Linear Optocoupler Circuit (48). The linear optocoupleris a four quadrant device which is built around the IL300. The threehigh side (50) lines a_(p), b_(p) and c_(p) are isolated by the linearoptocoupler and supplies isolated low side (49) lines a_(pi), b_(pi) andc_(pi) to be fed to the A/D of the DSP.

The said DSP program utilises these isolated sampled phase voltages toefficiently start and commutate the Brushless DC motor. The isolation ofboth output and input DSP lines along the dotted line I of FIG. 17ensures safe and proper operation of the programmed Digital SignalProcessor and DSP

The detailed analysis and operation of the DSP program to execute thepresent invention and operate the drive of FIG. 17 in an efficientmanner will now be performed.

The said DSP program developed for the implementation of the presentinvention for efficient starting, commutation and continuous operationof the Brushless DC motor includes the following features:

-   -   (a) a routine for parking the rotor at a known position for        efficient starting of the motor in the desired direction of        rotation,    -   (b) a routine for the computation of the BEMF Space Vector,    -   (c) a method to calculate the angle that the BEMF Space Vector        makes with the real axis,    -   (d) an indicator to detect the sector in which the BEMF Space        Vector is located in order to avoid divisions which results        exceed 2 and perform the inverse under these conditions,    -   (e) provisions to set two of the six DSP output lines high, in        order to turn on an upper and a lower transistor in different        legs of the inverter circuit, for connection of two phase        windings to the dc supply when a particular angle is reached by        the BEMF Space Vector, and,    -   (f) provisions for disabling BEMF Space Vector angle detection        when three phase windings are connected to the dc supply during        the commutation interval.

All these functions are included in the program flow charts of FIGS. 18a-18 e which are used for the implementation of the present invention'scommutation technique for efficient starting, commutation and continuousoperation of the three-phase Brushless DC motor under any loadcondition. The following analysis refers to a Brushless DC motor havingan unskewed rotor.

The flow chart in FIG. 18 a begins with the initialisation of allvariables by setting them to their initial starting values. Two programvariables, Parking_Count and PWM_Count were given initial values of 5000and 4 respectively. The program then flows to Main, where it keepscycling there until a PWM interrupt occurs. On the occurrence of a PWMinterrupt, a Parking Flag is checked to determine if the motor has beenparked. If the flag is not set, this indicates that the motor has notbeen parked and the program proceeds to park the motor in a knownposition before executing the Calculation and Running routines.

From FIG. 14, if the first pair of windings to be energised in theRunning routine is ac, then for efficient starting of the motor, and forrotation in the anti-clockwise direction, the rotor must be parked atthe position where the d-axis is at θ=0°. This parking position isaccomplished by energising windings cb in the Parking routine, whichaligns the north pole of the rotor magnet flux {right arrow over(φ_(m))} with the stator flux vector {right arrow over (φ_(cb))}. Sincethe said rotor takes some time to park and settle, where this time isdependent on the rotor inertia, motor load, rotor position beforeparking and the applied motor parking voltage, Parking_Count isdecremented each time the program executes this Parking routine. TheParking_Count value is checked to determine if its value is zero, and ifthe response is NO, the program returns to Main via the RTI command,where it will loop in main until a PWN interrupt is detected. On theoccurrence of another PWM interrupt which occurs every 50 μs on the ADMC401 DSP, the Parking Flag is checked, and since Parking_Count is not yetzero, the Parking Flag would not be set. The program therefore keepsenergizing windings cb until Parking_Count has decremented to the valueof zero. When this occurs, the Parking Flag is set and Windings_Count isset to 2. The program returns to Main and keeps looping there until thenext PWM interrupt occurs.

On the occurrence of this PWM interrupt, since the Parking Flag is set,the program would have completed the Parking routine and would bedirected to the Calculation routine via (52) as shown in FIG. 18 b. Inthe Calculation routine, the three analog to digital (ADC) linescarrying motor phase voltages v_(an), v_(bn), and v_(cn) are read. Sincethe motor is at standstill and windings cb are energized in the parkedposition, then the phase voltages supplied by the Phase Voltage SensingCircuit (51) via the Linear Optocoupler (48) to the ADC in FIG. 17 are:v_(an)=0, v_(bn)=−V/2 and v_(cn)=V/2. These three phase voltages v_(an),v_(bn) and v_(cn) are then projected on the magnetic axes of theirrespective phase windings whose directions are given by e^(j0)°,e^(j120)° and e^(j240)° respectively. Following this, the three phasevoltage vectors are added vectorially to produce the BEMF Space Vector{right arrow over (V_(R))}, whose real and imaginary parts are given byX and Y respectively. The location of positive magnetic axes forwindings aa′, bb′ and cc′ having an unskewed rotor magnet are shown inFIG. 19 a, while the BEMF Space Vectors for winding commutation and thevalue of Ratio at the angles for winding commutation are shown in FIG.19 b.

The Windings_Count value is then checked in the Calculation routine andthe program flows to one of two paths, depending on the Windings_Countvalue. Since after parking Windings_Count was set to 2, the programflows along the path 1, 2, 4, or 5 to determine the value of Ratio whichis given by

${\frac{Y}{X}}.$

Windings_Count is checked again in order to direct program progressionto one of the six routines of Windings_Count 1, 2, 3, 4, 5 or 6, therebycompleting the Calculation routine.

Since Windings_Count was set to 2 in the Parking routine, then theprogram jumps to execute Windings_Count 2 Running routine via (54) inFIG. 18 c. This running winding energization routine begins bydecrementing PWM_Count whose initial value is 4. The program then checksthe PWM_Count value to determine if it is zero. Since this is the firstdecrement of PWM_Count, its value would be 3, causing the first pair ofwindings to be energized in the Running routine to be ac.

The energization of windings ac produces stationary flux vector {rightarrow over (φ_(ac))}, which interacts with rotor flux vector {rightarrow over (φ_(m))} to develop electromagnetic torque in the motor, thuscausing the motor to start rotating in the anti-clockwise direction.After the energization of windings ac, the program returns to Main inFIG. 18 a and awaits a PWM interrupt. On the occurrence of a PWMinterrupt, since the Parking Flag is set, the program executes the BEMFSpace Vector Calculation routine in FIG. 18 b to determine the real andimaginary parts of the BEMF Space Vector produced. Rotation of the rotoron starting induces a BEMF in the unenergized winding aa′, thus allowingthe BEMF Space Vector to contain rotor position information. The programthen checks the Windings_Count value which is set to 2, performs Ratiocalculation of

${\frac{Y}{X}},$

then jumps to the Windings_Count 2 Running routine via (54) in FIG. 18 cIt proceeds to energize windings ac for four PWM interrupts and avoidschecking the value of Ratio during this time, since PWM_Count is not yetequal to zero.

The inclusion of: setting PWM_Count to 4, decrementing PWM_Count, andckecking PWM_Count for zero, serves to inhibit Ratio checking for 4 PWMcycles at the beginning of the starting process and during commutationof a winding. The purpose of these program blocks during starting wouldbe discussed here, and their function when the motor is running andwinding commutation is taking place will be discussed later. When themotor is parked, no BEMF is generated in the windings and a BEMF SpaceVector does not exist, but a resultant stationary voltage vector isproduced. It must be noted, that this resultant stationary voltagevector does not contain rotor position information. On entering theWindings_Count 2 Running routine in FIG. 18 c for the first time, theangle information

${\frac{Y}{X}},$

due to this resultant stationary voltage vector is prevented from beingdetected for up to four PWM cycles, until such time that the rotorbegins moving and a BEMF Space Vector is produced. When four PWMinterrupts have taken place, PWM_Count is set to zero and the programproceeds to set PWM_Count to 1 and checks Ratio to determine if itexceeds 1.732. When Ratio exceeds 1.732, the angle made by the BEMFSpace Vector and the real axis is greater than 60°, which implies thatwinding aa′ must be commutated and windings bc must be placed across thedc supply.

If however Ratio is less than 1.732 in this Windings_Count 2 Runningroutine, then the BEMF Space Vector has not reached the angle of 60°with the real axis and windings ac must remain energized until such timethat this happens. Since only four PWM interrupts have occurred, therotor would not have moved through 60° and the response to the Ratioblock would be No, causing windings ac to remain energized. The programthen returns to Main in FIG. 18 a and continues through the path of Yesfor Parking Flag, 2 for Windings_Count in the Calculation routine ofFIG. 18 b and then to the Windings_Count 2 Running routine of FIG. 18 c.When it reaches the Decrement PWM_Count block, since PWM_Count was setto 1, it would be decremented to zero. Hence, program progression is viathe Yes path of the “Is PWM_Count=0?”

If Ratio is greater than 1.732, then the BEMF Space Vector makes anangle greater than 60° with the real axis, indicating that winding aa′must be commutated and windings bc must be connected to the dc supply.Hence, program progression moves along the Yes path of “Is Ratio>1.732?”block and Windings_Count is incremented to the value of 3 to shiftoperation from Windings_Count 2 Running routine to Windings_Count 3Running routine in FIG. 18 d. PWM_Count is set to 4 and then windings bcare energized. The program then returns to Main in FIG. 18 a to await aPWM interrupt.

When the PWM interrupt occurs, program progression is via Yes of the“Check If Parking Flag Is Set” block to the Calculation routine in FIG.18 b and along the path “If 3 or 6” of the “Check Windings_Count” block,since Windings_Count is now set to 3. Ratio of real/imaginary values arenow calculated instead of imaginary/real. The reason for this is asfollows: As the BEMF Space Vector rotates in an anti-clockwisedirection, for angles greater than 60° with the real axis, the ratio ofimaginary to real becomes very large. This is because the real valueapproaches zero as the BEMF Space Vector approaches the positive andnegative imaginary axes.

For values of the numerator much greater than that of the denominator inthe division process, the DSP utilises a large number of clock cycles tocompute the division. Hence the 50 μs duration between PWM interruptsdoes not provide sufficient time for divisions producing large resultsand performing all other tasks. The division routine time issignificantly reduced when the BEMF Space Vector exceeds 60° with thereal axis by computing real/imaginary when Windings_Count is 3 and 6.Having executed the real/imaginary division to computer Ratio, theprogram checks Windings_Count again and jumps to the Windings_Count 3Running routine via (55) in FIG. 18 d.

If the motor is operating under load, then although windings bc areenergized in the Windings_Count 2 Running routine of FIG. 18 c, windingaa′ would not have commutated its current, and would still be connectedto the dc supply via anti-parallel diode D₄ as shown in FIG. 12. Underthese conditions a resultant voltage vector shown in FIG. 14 isproduced. This resultant voltage vector does not possess rotor positioninformation and moves through 60° in an anti-clockwise direction at thebeginning of the commutation interval, then rotates backwards in aclockwise direction for less than 60°, depending on the current in thecommutating winding aa′ before commutation began. Hence, the “DecrementPWM_Count” and “Is PWM_Count=0?” blocks in the Running routines ensurethat program progression is via the No path of the “Is PWM_Count=0?”block, thus preventing Ratio checks to be performed for four PWM cycles.This serves enough time for winding aa′ to commutate its largest currentwhich occur under full load conditions. Therefore the new windings bcare energized for four PWM cycles in FIG. 18 d before the ratio ofreal/imaginary is checked. After the four PWM cycles have elapsed,PWM_Count would be zero, allowing program progression along the Yes pathof the “Is PWM_Count=0?” block, thus allowing Ratio to be checked tointroduce the new winding pair when Ratio is greater than 0.5774.Otherwise, windings bc would be kept energized. When Ratio becomesgreater than 0.5774, Windings_Count is incremented to 4 and PWM_Count isset to 4. The new pair of windings ba is energized and the programreturns to Main in FIG. 18 a where it loops and awaits a PWM interrupt.When a PWM interrupt occurs, program progression is through theCalculation routine in FIG. 18 b and via “If 1, 2, 4 or 5” path forratio calculation of

$\frac{Y}{X}$

before jumping to the Windings_Count 4 Running routine via (56) of FIG.18 d. This said Running routine differs from the others in that thecheck block for energization of the new windings in this routine doesnot look for a ratio, but checks for a sign change between new andprevious values of Y. This check is performed in this routine becausewhen the BEMF Space Vector crosses the real axis, the new windings camust be connected to the dc supply and the current in winding bb′ mustbe commutated.

The program continues executing Windings_Count 5 via (57) andWindings_Count 6 via (58) Running routines in FIG. 18 e for theenergization of windings ca and cb respectively. When Ratio is greaterthan 0.5774 in the Windings_Count 6 Running routine, Windings_Count isnot incremented as was previously done in all other Running routines,but it is set to 1, thereby directing the program to the Windings_Count1 Running routine via (53) of FIG. 18 c to begin a new cycle of Runningroutines.

The flow chart structure shown in FIGS. 18 a-18 e ensures that all thefeatures (a) through (f) listed at the beginning of this section aretaken into consideration for efficient starting and running of theBrushless DC motor under all load conditions.

Table 5 summarizes the activities occurring when the BEMF Space Vectorreaches an angle for the introduction of a new winding pair to the dcsupply. The state of the DSP output lines and the transistors to beturned on in the Inverter Circuit are also given.

TABLE 5 Value of DSP BEMF Wind- Ratio EX. Out- Inverter Space ing ForNew put Transistors New Vector Count Ratio Windings Lines TurnedWindings Angle α Value Chosen Energization High On Energized α > 0° 2$\frac{Y}{X}$ >1.732 a⁺ c⁻ Q1 & Q2 ac α > 60° 3 $\frac{X}{Y}$ >0.5774b⁺ c⁻ Q3 & Q2 bc α > 120° 4 None Sign Change b⁺ a⁻ Q3 & Q4 ba In Y α >180° 5 $\frac{Y}{X}$ >1.732 c⁺ a⁻ Q5 & Q4 ca α > 240° 6$\frac{X}{Y}$ >0.5774 c⁺ b⁻ Q5 & Q6 cb α > 300° 1 None Sign Change a⁺ b⁻Q1 & Q6 ab In Y α > 360° 2 $\frac{Y}{X}$ >1.732 a⁺ c⁻ Q1 & Q2 ac

It was observed earlier that for the skewed rotor to produce BEMFs inphase with that of the unskewed rotor, the stator windings must berotated by half the skew angle, thereby rotating the magnetic axes ofthe windings by the same amount and in the same direction. The rotationof the magnetic axes as a result of a rotor magnet skew of β=20° isshown in FIG. 20 a. Since the phase voltages and BEMFs all lie along themagnetic axes of the phase windings, then the BEMF Space Vectorsresponsible for commutation of phase windings lie alone the lines fromthe center of the hexagon to the vertices and are depicted in the 10°clockwise skewed hexagon of FIG. 20 b. FIG. 20 b also shows the ratiosof

$\frac{Y}{X}$

and

$\frac{X}{Y}$

examined for commutation of phase windings.

The flow charts used for implementation of the present invention for aβ=20° skewed rotor are presented in FIGS. 21 a-21 e.

The Parking routine for the unskewed and skewed rotors differ by theinitialisation of one additional variable “Set Greater_(—)75=1” in theskewed Parking routine of FIG. 21 a. Hence the operation of the Parkingroutine given earlier for the unskewed rotor applies for the skewedrotor.

The Calculation routine for the unskewed rotor differs from that of theskewed rotor in FIG. 21 b in the position of the positive magnetic axesproduced. Since the positive magnetic axes of windings aa′, bb′ and cc′take up positions of e^(−j10)°, e^(j110)° and e^(j230)° respectively,then the BEMF Space Vector produced with the skewed rotor must reflectthese positions in the Calculation routine. Other than this difference,the two Calculation routines are identical and the explanation given forthe operation of the unskewed Calculation routine applies to that forthe skewed rotor Calculation routine. Flow from the Parking routine tothe Calculation routine is via (59) in FIG. 20 a.

The Running routines of the unskewed rotor are similar to those of theskewed rotor except for the different values of Ratio examined in eachRunning routine due to the skewing of the rotor and the two new Runningroutines for Windings_Count 3 and 6 of FIG. 21 d and FIG. 21 erespectively. The operation of Running routines for Windings_Count 1, 2,4 and 5 for the skewed rotor in FIGS. 21 a-21 e only differ from thoseof the unskewed rotor of FIGS. 18 a-18 e by the values of Ratioexamined, and Ratio is checked in Running routines for Windings_Count 1and 4 for the skewed Running routine of FIGS. 21 a-21 e instead of thesign change in Y for the unskewed Running routines of FIGS. 18 a-18 e.Hence, the operation of the unskewed Running routines for Windings_Count1, 2, 4 and 5 of FIGS. 18 a-18 e applies for those of the skewed Runningroutines of FIGS. 21 a-21 e. Progression from Calculation routine toRunning routines is via (60) for Windings_Count 1 Running routine, via(61) for Windings_Count 2 Running routine, via (62) for Windings_Count 3Running routine, via (63) for Windings_Count 4 Running routine, via (64)for Windings_Count 5 Running routine and via (65) for Windings_Count 6Running routine.

However, Running routines for Windings_Count 3 and 6 in FIGS. 21 a-21 eare entirely different from those of the unskewed rotor in FIGS. 18 a-18e, and the explanation of their operation is now presented. WhenWindings_Count is incremented to 3 in the Windings_Count 2 Runningroutine of FIG. 21 c, the program flows to the Windings_Count 3 Runningroutine of FIG. 21 d via the Calculation routine of FIG. 21 b on theoccurrence of a the next PWM interrupt. It must be noted that onentering the Windings_Count 3 Running routine of FIG. 21 d, the BEMFSpace Vector {right arrow over (V_(R2))} is produced, at position 1 (68)in FIG. 22, which makes an angle of 50° with the real positive axis (66)and is rotating in an anti-clockwise direction. Since Windings_Count is3,

$\frac{X}{Y}$

is computed for the Ratio value in this Windings_Count 3 Running routineof FIG. 21 d.

The next commutation takes place when the BEMF Space Vector {right arrowover (V_(R3))} is produced, at position 4 (71) in FIG. 22, which makesan angle of 70° with the real negative axis or 20° with the imaginarypositive axis (67). The

$\frac{X}{Y}$

ratios at positions 1 and 4 are 0.8391 and 0.3639 respectively. As theBEMF Space Vector moves from positions 1 to 4 traversing 60°, the ratioof 0.3639 is reached at position 2 (69), at which point it makes anangle of 20° to the right of the imaginary positive axis (67). Sincepositions 2 and 4 of the BEMF

Space Vector have the same Ratio value, with position 4 being thecorrect commutation point, Ratio checking must be inhibited up to thepoint when the BEMF Space Vector is at position 3 (70), where it makesan angle of 15° on the right of the imaginary positive axis (67).

These issues are included in Running routines for Windings_Count 3 and 6shown in FIGS. 21 a-21 e. On entering the Windings_Count 3 Runningroutine of FIG. 21 d, PWM_Count is not decremented and checked for zeroas was done in the four Running routines for Windings_Count 1, 2, 4 and5 for the unskewed rotor in FIGS. 18 a-18 e. This process causedinhibiting of Ratio checking when the resultant voltage vector, whichdoes not possess rotor position information is produced duringcommutation of winding aa′ is taking place at the beginning of thisRunning routine. However, this function produced by the “DecrementPWM_Count” and “Is PWM_Count=0?” blocks in the Running routines for theunskewed rotor of FIGS. 18 a-18 e are produced by the blocks that followin the Windings_Count 3 Running routine of the skewed rotor of FIG. 21d. On entering the Windings_Count 3 Running routine of FIG. 21 d,Greater_(—)75 which was set to 1 in the initialisation stage of theParking routine of FIG. 21 a is checked for zero. Since no change hasoccurred to Greater_(—)75, the program flows to check if Ratio is lessthan 0.2679.

This Ratio check of 0.2679, which represents a BEMF Space Vectorlocation at position 3 (70) of FIG. 22, ensures that Ratio is onlychecked after the BEMF Space Vector has passed position 2 (69) in FIG.22. This Ratio check of 0.2679 serves two purposes. It ensures thatwinding cc′ is not commutated at the incorrect point when the rotor hasonly moved through 20° after the last commutation and it also ensuresthat Ratio is not checked when the resultant voltage vector is producedduring commutation of winding aa′. If ratio is not less than 0.2679,then the Ratio value of 0.3639 is not checked and the program proceedsto continue energization of windings bc, execute a RTI command andreturn to the Windings_Count 3 Running routine on the occurrence ofanother PWM interrupt.

Since Greater_(—)75 is not zero, the program checks if Ratio is lessthan 0.2679 and if it is, said program sets Greater_(—)75 to zero andchecks if Ratio is greater than 0.3639. If Ratio is not greater than0.3639, said program proceeds to energize windings bc, executes the RTIcommand and return to the Windings_Count 3 Running routine on theoccurrence of a PWM interrupt. Since Greater_(—)75 is now zero, saidprogram checks if Ratio is greater than 0.3639. If it is, said programincrements Windings_Count, energizes the new pair of windings ba, setsGreater_(—)75 to 1 and executes the RTI command. On the next PWMinterrupt, said program is directed to the Windings_Count 4 Runningroutine of FIG. 21 d.

Windings_Count 6 Running routine in FIG. 21 e is similar to that ofWindings_Count 3 Running routine of FIG. 21 d, except that “IncrementWindings_Count To Energize ab” is replaced with “Set Windings_Count=1 ToEnergize ab”. This replacement is due to the fact that theWindings_Count 6 Running routine is the last in the set of Runningroutines and said program must be directed to the Windings_Count 1Running routine of FIG. 21 c to begin a new Running routine cycle.

Table 6 summarises the activities occurring when the BEMF Space Vectorreaches an angle for the commutation of a winding and the introductionof a new winding pair to the dc supply. The state of the DSP outputlines and the transistors to be turned on in the Inverter Circuit arealso given.

TABLE 6 Value of DSP BEMF Wind- Ratio EX. Out- Inverter Space ing ForNew put Transistors New Vector Count Ratio Windings Lines TurnedWindings Angle α Value Chosen Energization High On Energized α > ⁻10° 2$\frac{Y}{X}$ >1.1918 a⁺ c⁻ Q1 & Q2 ac α > 50° 3 $\frac{X}{Y}$ >0.3639b⁺ c⁻ Q3 & Q2 bc α > 110° 4 $\frac{Y}{X}$ <0.1732 b⁺ a⁻ Q3 & Q4 ba α >170° 5 $\frac{Y}{X}$ >1.1918 c⁺ a⁻ Q5 & Q4 ca α > 230° 6$\frac{X}{Y}$ >0.3639 c⁺ b⁻ Q5 & Q6 cb α > 290° 1 $\frac{Y}{X}$ <0.1732a⁺ b⁻ Q1 & Q6 ab α > 350° 2 $\frac{Y}{X}$ >1.1918 a⁺ c⁻ Q1 & Q2 ac

While the present invention has been herewithin described, withreference to a preferred embodiment or embodiments, it will berecognized by those aptly skilled in the art, that the innovative andground-breaking concepts heretofore disclosed in the presentapplication, can be modified and varied over a tremendous range ofapplications and that various changes may be made and equivalents may besubstituted for elements thereof, without departing from the scope ofthe present invention.

In consequence therefore, it is intended that the invention not belimited to the particular embodiment or embodiments as disclosedherewithin, as the best mode contemplated for carrying out of thepresent invention, but that the invention shall include this and allembodiments, howsoever found, mutatis mutandis, falling within the scopeof the appended claims.

1. A system for operating a brushless DC motor, said system comprising:a brushless DC motor; a processor capable of determining a BEMF SpaceVector; and a processor capable of determining the angle that the BEMFSpace Vector makes with the real axis.
 2. The system of claim 1 whereinthe processor capable of determining the BEMF space vector is the sameas the processor capable of determining the angle that the BEMF SpaceVector makes with the real axis.
 3. The system of claim 1 wherein theprocessor capable of determining the BEMF space vector is different fromthe processor capable of determining the angle that the BEMF SpaceVector makes with the real axis.
 4. The system in claim 1 whereindetermination of the BEMF Space Vector is performed by addition of phasevoltage vectors of the energized windings and the BEMF vector of theunenergized winding.
 5. The system in claim 1 further includingprovisions for disabling angle determination during a commutationinterval in which a resultant voltage vector is produced that does notpossess rotor position information.
 6. A method of commutating anelectric motor comprising rotating the rotor in only a clockwisedirection or only an anticlockwise direction.
 7. The method of claim 6further comprising determining the position of a rotor of a brushless DCmotor.
 8. The method of claim 6 further comprising summing phase windingvoltage vectors of energized windings with the BEMF vector of anunenergized winding to determine a BEMF Space Vector and determining anangle that the BEMF Space Vector makes with the real axis.
 9. The methodof claim 6 further comprising energizing and deenergizing phase windingsbased on the position of the BEMF space vector.
 10. The method of claim6 wherein voltage vectors are determined by projection of detected phasewinding voltages along the phase winding's magnetic axis.
 11. The methodof claim 6 wherein the angle that the BEMF Space Vector makes with thereal axis is determined using the ratio of the real value of the BEMFSpace Vector to the imaginary value of the BEMF Space Vector or theinverse ratio thereof.
 12. The method of claim 6 wherein the motor is aDC motor that includes a plurality of phases and a plurality of poles.13. The method of claim 6 wherein the phase winding voltage vectors areproduced by the referral of the scalar phase voltages in electriccircuits to magnetic axes in the corresponding magnetic circuits thatare a result of the equality of scalar electric and vector magneticcurrent magnitudes.
 14. The method of claim 6 wherein the BEMF SpaceVector rotates at the same speed as that of the rotor and provides rotorposition information determined using the angle that the BEMF SpaceVector makes with the real positive axis.
 15. The method of claim 6wherein the rotor position information is used to commutate phasewindings.